faces. (The means were 3.26 and 2.64, respectively.) But notice also that the ratings for the
composites of 32 faces are considerably more homogeneous than the ratings of the com-
posites of four faces. Figure 2.13 plots these sets of data as standard histograms.
Even though it is apparent from Figure 2.13 that there is greater variability in the rating
of composites of four photographs than in the rating of composites of 32 photographs,
some sort of measure is needed to reflect this difference in variability. A number of meas-
ures could be used, and they will be discussed in turn, starting with the simplest.Range
The rangeis a measure of distance, namely the distance from the lowest to the highest
score. For our data, the range for Set 4 is (4.02 2 1.20) 5 2.82 units; for Set 32 it is (3.38 2
3.13) 5 0.25 unit. The range is an exceedingly common measure and is illustrated in every-
day life by such statements as “The price of red peppers fluctuates over a 3-dollar range
from $.99 to $3.99 per pound.” The range suffers, however, from a total reliance on extreme
values, or, if the values are unusually extreme, on outliers. As a result, the range may give a
distorted picture of the variability.Interquartile Range and Other Range Statistics
The interquartile rangerepresents an attempt to circumvent the problem of the range’s
heavy dependence on extreme scores. An interquartile range is obtained by discarding the38 Chapter 2 Describing and Exploring Data
Table 2.6 Rated attractiveness of composite faces
Set 4 Set 32
Composite Composite
Picture of 4 Faces Picture of 32 Faces
1 1.20 21 3.13
2 1.82 22 3.17
3 1.93 23 3.19
4 2.04 24 3.19
5 2.30 25 3.20
6 2.33 26 3.20
7 2.34 27 3.22
8 2.47 28 3.23
9 2.51 29 3.25
10 2.55 30 3.26
11 2.64 31 3.27
12 2.76 32 3.29
13 2.77 33 3.29
14 2.90 34 3.30
15 2.91 35 3.31
16 3.20 36 3.31
17 3.22 37 3.34
18 3.39 38 3.34
19 3.59 39 3.36
20 4.02 40 3.38
Mean 5 2.64 Mean 5 3.26range
interquartile
range